If there was some sort of predictable doubling of price, speculation would simply immanentize such price changes, discounted for the market's time value. So it would be a vertical price change.

Not exactly, for three reasons.

1) Predictable by some is not predictable by others. Especially, many people do not yet understand Bitcoin or its growth potential. It seems to take newbies several months before they understand it enough to be comfortable investing in it, and the learning curve can be much longer for the less tech-savvy or less economics-savvy.

2) Short-term volatility throws people off.

3) Most subtly, and I think this is the point that the technical analysts miss: with Bitcoin, "the market" is not a static number of people, but a constantly growing one. Since this growth is mediated by the network effect, the growth of "the market" (the totality of people who have even heard of BTC and take it seriously, know how to buy it and keep it, and are qualified to evaluate BTC as an investment) may well be exponential.

Yeah, nothing is assured. Even if it continues in a near-perfect exponential run for another six months and is at $800 or something, a glitch or government crackdown or exchange hack could send the price down into the nether-reaches again. There is no guarantee, and although the upside potential isn't so hard to get a handle on, it takes people quite a while to ascertain the potential risks.

"This" (today) is too short-term to tell, but overall since I posted the OP a few months ago the "fast exponential run-up" scenario seems to be playing out to a tee.

"Needless to say, it'd be a white-knuckle roller coaster ride with plenty of euphoria and ample gut-spilling scares. Millionaires and billionaires would be born, profits would be taken heartily all the way up, bubbles would be called constantly, and many would miss the train - perhaps multiple times. Most of all people would be wondering WTF was going on, endless theories would be postulated and debated."

Well the ultra-fast exponential run-up scenario didn't play out like I fantasized here (it was just an interesting possibility). It may have continued for quite a while longer if not for MtGox getting swamped, and it's possible that it's just delayed until now, but considering some other parameters - like how long it will take for infrastructure and user-friendliness to reach the level required for mainstream adoption - it would be impossible to continue at the Spring 2013 pace for very long.

I now think what happened was that the 2011 crash burned in people's memories left the price languishing too low for too long, and Spring 2013 was the upward correction of that. There may be more upward correcting to do, but either way I still absolutely believe that Bitcoin is on an exponential growth path. Just a slower one. Tenfold per year seems about right, since that jives with history and also allows 3-5 years for full mainstream adoption to happen, which seems not too unreasonable.

Or maybe even up to 7-10 years considering the exponential curve would turn toward an S-curve midway through mainstream adoption. But anyway, within 5 years if Bitcoin is going to do its thing it's going to be a totally different world we're living in, with anyone who has any today-decent amount of coins being very wealthy then (unless they panic sell, and most of course will ).

10x per year is still a very fast rate that will cause all the things I mentioned in the OP to happen, as can be seen from looking over the history of this forum, even if it's much slower than the 10x per season we had Jan-April 2013.

Personally, the price is not rising all that fast all things considered. I don't think we are in a bubble yet. For some exponential growth we would need to see some $1,000 per week growth. A few hundred dollars a month growth here and there just seems low to me. Maybe someone can post a real life asset that went from 1k to 30k in a short time and what the rise looked like.

Personally, the price is not rising all that fast all things considered. I don't think we are in a bubble yet. For some exponential growth we would need to see some $1,000 per week growth. A few hundred dollars a month growth here and there just seems low to me. Maybe someone can post a real life asset that went from 1k to 30k in a short time and what the rise looked like.

Define a "short time" first.If 11 years is short time, then check out BRK-A chart between 1982 and 1993.It went from $475 to $17525 (similar to a move between $1k and 30K)https://finance.yahoo.com/chart/BRK-Achoose interactive, then logarithmic

Typically, financial assets don't have many thou of $ value per most used unit of measurement.BTC would have to move first to millies (mbtc), then bits, then, maybe even satoshi's.